Yes, front and rear wheels have 32 spokes.

The shifting with the Sunrace cassette is really excellent, it cannot be better with the Shimano cassette.

As said, for me 52x11 is too short, its what I had from factory on my Titanium Birdy. R&M always mounted cassettes with 9t smallest cog on the Birdy. I wouldn't invest in a new hub and spokes for a hub that cannot accept cogs smaller than 11t for the Birdy.

For the chain, KMC chain X10SL or X11SL Gold TiN are much better than any Shimano chain, weight less, last longer, excellent factory lubrication.

To fit the Birdy in a big Samsonite case, I think you will have to dismount the front wheel and probably the rear mudguard.

About the disc, since my rear hub is also centerlock, I mounted a centerlock Shimano XT RT-MT800 Ice technology disc and its makes much more noise than the original SM-RT56 disc !

For the front wheel, the Birdy has its disc on the right side what is very unusual.

Most discs are designed to turn in one direction, i.e. counterclockwise. When mounting the disc on the right side, if the disc isn't flipped, it will turn clockwise which will cause problems. Only one piece steel discs like the original SM-RT56 can be flipped. Discs with a center aluminum star cannot be flipped and will turn in the wrong direction.